Questions: Compound X has a molar mass of 416.41 g/mol and the following composition: element mass % phosphorus 14.88 % chlorine 85.12 % Write the molecular formula of X.

Solution Steps

First, we need to calculate the number of moles of each element in 100 grams of compound $X$.

• Phosphorus (P):
  $$\text{Mass of P} = 14.88 \, \text{g}$$ The molar mass of phosphorus is approximately $30.97 \, \text{g/mol}$. $$\text{Moles of P} = \frac{14.88 \, \text{g}}{30.97 \, \text{g/mol}} = 0.4805 \, \text{mol}$$

• Chlorine (Cl):
  $$\text{Mass of Cl} = 85.12 \, \text{g}$$ The molar mass of chlorine is approximately $35.45 \, \text{g/mol}$. $$\text{Moles of Cl} = \frac{85.12 \, \text{g}}{35.45 \, \text{g/mol}} = 2.4017 \, \text{mol}$$

Next, we find the simplest whole number ratio of moles of phosphorus to moles of chlorine.

• Ratio of P to Cl: $$\text{Ratio} = \frac{0.4805}{0.4805} : \frac{2.4017}{0.4805} = 1 : 5$$

The empirical formula is based on the simplest whole number ratio of moles of each element. From the ratio calculated, the empirical formula is $\text{PCl}_5$.

To find the molecular formula, we compare the molar mass of the empirical formula with the given molar mass of compound $X$.

• Molar Mass of Empirical Formula $\text{PCl}_5$: $$\text{Molar mass of } \text{PCl}_5 = 30.97 + 5 \times 35.45 = 208.22 \, \text{g/mol}$$

• Molecular Formula: $$\text{Factor} = \frac{416.41}{208.22} \approx 2$$

Thus, the molecular formula is $\text{P}_2\text{Cl}_{10}$.

Final Answer